An outline of ergodic theory by Steven Kalikow

This casual advent specializes in the department of ergodic thought often called isomorphism conception. workouts, open difficulties, and important tricks actively have interaction the reader and inspire them to take part in constructing proofs independently. perfect for graduate classes, this publication is usually a worthwhile reference for the pro mathematician.

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This publication offers an advent to localised excitations in spatially discrete structures, from the experimental, numerical and mathematical issues of view. sometimes called discrete breathers, nonlinear lattice excitations and intrinsic localised modes; those are spatially localised time periodic motions in networks of dynamical devices.

We also say that the system ( , A , μ , T ) is a factor of the system ( , A, μ, T ), and that the system ( , A, μ, T ) is an extension of the system ( , A , μ , T ). 131. Definition. Let ( , A, μ, T ) and ( , A , μ , T ) be measure-preserving is a homomorphism. If there systems and assume that π : → such that the restriction of exist full measure sets X ⊂ and X ⊂ π to X is a bimeasurable bijection between X and X , we say that π is an isomorphism and that the systems ( , A, μ, T ) and ( , A , μ , T ) are isomorphic.